We have verified the above physical picture by performing 1D/2D PIC simulations with OSIRIS [1]}. A wide range of parameters are examined, including the dependences of \(\alpha \) , \(n_i\)  (\(Z_i\)  is set to be 1 for simplicity), angle \(\theta \)  and pair temperature \(T_p\) . In the 1D simulations, the spatial and temporal resolutions are \(\Delta x=1.8\times 10^{-4}\lambda _0\)  and \(\Delta t=1.6\times 10^{-4}T_0\) , where \(T_0=2\pi \omega _{0}^{-1}\)  is the laser period. The mixed target is placed at \(127c/\omega _0 \leqslant x\leqslant 190c/\omega _0\) . A short-pulse laser is initialized in the box with a profile of \(a_0\sin ^2(\pi t/\tau _0)\)  where \(a_0=0.5\)  and \(\tau _0=20T_0\) . Meanwhile, simulations with pure electron-ion plasmas are performed for comparison, to verify that the observed physics is due to the positron population. Convergence tests with higher resolutions have been performed showing the same results as presented here.
